Towards an Efficient Bisection of Ellipsoids

  • Paden Portillo
  • Martine Ceberio
  • Vladik Kreinovich
Part of the Studies in Computational Intelligence book series (SCI, volume 539)

Abstract

Constraints are often represented as ellipsoids. One of the main advantages of such constrains is that, in contrast to boxes, over which optimization of even quadratic functions is NP-hard, optimization of a quadratic function over an ellipsoid is feasible. Sometimes, the area described by constrains is too large, so it is reasonable to bisect this area (one or several times) and solve the optimization problem for all the sub-areas. Bisecting a box, we still get a box, but bisecting an ellipsoid, we do not get an ellipsoid. Usually, this problem is solved by enclosing the half-ellipsoid in a larger ellipsoid, but this slows down the domain reduction process. Instead, we propose to optimize the objective functions over the resulting half-, quarter, etc., ellipsoids.

Keywords

constraints ellipsoids bisection computational complexity 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Paden Portillo
    • 1
  • Martine Ceberio
    • 1
  • Vladik Kreinovich
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

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